R for Art Sundays
Mandalas + Galaxies = Mandalaxies
An R experiment to create images generated by the trajectory of a particle according to some equations.
Made with Rcpp, tidyverse
Blog post explaining the experiment: Mandalaxies
Inspired by: Strange Attractors: Creating Patterns in Chaos, by Julien C. Sprott
# Load packages
library(Rcpp)
library(tidyverse)
opt <- theme(legend.position = "none",
panel.background = element_rect(fill="black", color="black"),
plot.background = element_rect(fill="black"),
axis.ticks = element_blank(),
panel.grid = element_blank(),
axis.title = element_blank(),
axis.text = element_blank())
# Cpp function to build the dataframe according the equations
cppFunction('DataFrame createTrajectory(int n, double x0, double y0,
double a1, double a2, double a3, double a4, double a5,
double a6) {
// create the columns
NumericVector x(n);
NumericVector y(n);
x[0]=x0;
y[0]=y0;
for(int i = 1; i < n; ++i) {
x[i] = 10*a1+(x[i-1]+a2*sin(a3*y[i-1]+a4))*cos(2*M_PI/(13+10*a6))+y[i-1]*sin(2*M_PI/(13+10*a6));
y[i] = 10*a5-(x[i-1]+a2*sin(a3*y[i-1]+a4))*sin(2*M_PI/(13+10*a6))+y[i-1]*cos(2*M_PI/(13+10*a6));
}
// return a new data frame
return DataFrame::create(_["x"]= x, _["y"]= y);
}
')
# Parameters (change them to create your own mandalaxies)
a1 <- 3.3
a2 <- -3.7
a3 <- 4.5
a4 <- 2.1
a5 <- 0.3
a6 <- 3.5
# Number of points to draw
npoints <- 4000000
# Creation of the data frame
df <- createTrajectory(npoints, 0, 0, a1, a2, a3, a4, a5, a6)
# Plot
plot <- ggplot(df) +
geom_point(aes(x, y), shape=46, alpha=0.01, size=0, color="white") +
scale_x_continuous(expand = c(0,0))+
scale_y_continuous(expand = c(0,0))+
coord_fixed() + opt
plot